Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anj9)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=5, a₂>=5

For fixed z and a₁=5, a₂=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=-7/2

http://functions.wolfram.com/07.25.03.anj9.01

Input Form

HypergeometricPFQ[{5, 6}, {-(7/2), 1}, z] == (1/4838400) (4838400 - 41472000 z + 174182400 z^2 - 722534400 z^3 + 6502809600 z^4 + 21556000845 z^5 + 20486635500 z^6 + 8965764720 z^7 + 2114351280 z^8 + 287547680 z^9 + 23016768 z^10 + 1061120 z^11 + 25856 z^12 + 256 z^13) + (1/9676800) (E^z Sqrt[Pi] (25264228275 z^(9/2) + 58045086450 z^(11/2) + 48371317200 z^(13/2) + 19807135200 z^(15/2) + 4495658400 z^(17/2) + 597113280 z^(19/2) + 47069440 z^(21/2) + 2147840 z^(23/2) + 51968 z^(25/2) + 512 z^(27/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]